There is a lengthy wiki post in FlyerTalk Forums > Miles&Points > Credit, Debit and Prepaid Card Programs > Chase | Ultimate Rewards regarding Priority Pass.

Here's the basic information on how to get a Prioroty Pass if you have a Chase Sapphire Reserve card:

Basic Entry Information:
If you have never used a Priority Pass lounge click HERE to read how it works.

philemer's PP card arrived 20 days following approval of CSR. Others have reported an even quicker delivery. Yes, it comes via USPS.
Authorized User will receive their own PP card.

The PP Select membership offered through the CSR now includes digital pass access. Sign up in advance here: https://www.prioritypass.com/chasedmc
Note: Some lounges may not accept the digital pass. Make sure to check the PP lounge directory details for the specific lounge you plan on visiting.

To sign up for Priority Pass Select, as soon as the account shows up online:
1. Click on Go To Ultimate Rewards.
2. Scroll down to the very bottom left and click on "Card Benefits"
3. Activate Membership to request card.
4. Card can't be expedited. Some members have reported success in charging the lounge access to their CSR account and requesting a refund from Customer Service. However, others have reported that the lounge access was refunded via the travel credit.